| {"id": 1, "question": "The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The correct diameter of the sphere is", "response_choices": "(A) 3.07 cm (B) 3.11 cm (C) 3.15 cm (D) 3.17 cm", "answer": "C", "page_number": 1, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 2, "question": "An ideal gas undergoes a four step cycle as shown in the P \u2013 V diagram below. During this cycle, heat is absorbed by the gas in", "response_choices": "(A) steps 1 and 2 (B) steps 1 and 3 (C) steps 1 and 4 (D) steps 2 and 4", "answer": "B", "page_number": 1, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 3, "question": "An extended object is placed at point O, 10 cm in front of a convex lens L1 and a concave lens L2 is placed 10 cm behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are 20 cm. The refractive index of both the lenses is 1.5. The total magnification of this lens system is", "response_choices": "(A) 0.4, (B) 0.8, (C) 1.3, (D) 1.6", "answer": "(C) 1.3", "page_number": 2, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 4, "question": "A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is", "response_choices": "(A) 50, (B) 75, (C) 350, (D) 525", "answer": "(C) 350", "page_number": 2, "image_available": "no", "question_subject": "physics"} | |
| {"id": 5, "question": "The value of t is ___ .", "response_choices": "", "answer": "", "page_number": 3, "image_available": "no", "question_subject": "physics"} | |
| {"id": 6, "question": "The value of x is ___ .", "response_choices": "", "answer": "", "page_number": 3, "image_available": "no", "question_subject": "physics"} | |
| {"id": 7, "question": "In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q1 \u03bcC. Then S is switched to position Q. After a long time, the charge on the capacitor is q2 \u03bcC.", "response_choices": "", "answer": "", "page_number": 3, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 8, "question": "In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q1 \u03bcC. Then S is switched to position Q. After a long time, the charge on the capacitor is q2 \u03bcC.", "response_choices": "", "answer": "", "page_number": 3, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 7, "question": "The magnitude of q1 is ___ .", "response_choices": "", "answer": "", "page_number": 4, "image_available": "no", "question_subject": "physics"} | |
| {"id": 8, "question": "The magnitude of q2 is ___ .", "response_choices": "", "answer": "", "page_number": 4, "image_available": "no", "question_subject": "physics"} | |
| {"id": 9, "question": "The value of R is ___ meter.", "response_choices": "", "answer": "", "page_number": 4, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 10, "question": "The value of b is ___ meter.", "response_choices": "", "answer": "", "page_number": 4, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 13, "question": "A particle of mass M = 0.2 kg is initially at rest in the xy-plane at a point (x = -l, y = -h), where l = 10 m and h = 1 m. The particle is accelerated at time t = 0 with a constant acceleration a = 10 m/s^2 along the positive x-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by L and \u03c4, respectively. i, j and k are unit vectors along the positive x, y and z-directions, respectively. If k = i \u00d7 j then which of the following statement(s) is(are) correct?", "response_choices": "(A) The particle arrives at the point (x = l, y = -h) at time t = 2 s \n\n(B) \u03c4 = 2 k when the particle passes through the point (x = l, y = -h) \n\n(C) L = 4 k when the particle passes through the point (x = l, y = -h) \n\n(D) \u03c4 = k when the particle passes through the point (x = 0, y = -h)", "answer": "B", "page_number": 7, "image_available": "no", "question_subject": "physics"} | |
| {"id": 14, "question": "Which of the following statement(s) is(are) correct about the spectrum of hydrogen atom?", "response_choices": "(A) The ratio of the longest wavelength to the shortest wavelength in Balmer series is 9/5 \n\n(B) There is an overlap between the wavelength ranges of Balmer and Paschen series \n\n(C) The wavelengths of Lyman series are given by (1 + m^2/n^2) \u03bb0, where \u03bb0 is the shortest wavelength of Lyman series and m is an integer \n\n(D) The wavelength ranges of Lyman and Balmer series do not overlap", "answer": "C", "page_number": 7, "image_available": "no", "question_subject": "physics"} | |
| {"id": 15, "question": "A long straight wire carries a current, I = 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at distances 1 cm and 4 cm from the wire. At time t = 0, the rod starts moving on the rails with a speed v = 3.0 m/s (see the figure). A resistor R = 1.4 \u03a9 and a capacitor Co = 5.0 \u03bcF are connected in series between the rails. At time t = 0, Co is uncharged. Which of the following statement(s) is(are) correct? [\u03bco = 4\u03c0 \u00d7 10^-7 SI units. Take ln 2 = 0.7]", "response_choices": "(A) Maximum current through R is 1.2 \u00d7 10^-6 ampere\n\n(B) Maximum current through R is 3.8 \u00d7 10^-6 ampere\n\n(C) Maximum charge on capacitor Co is 8.4 \u00d7 10^-12 coulomb\n\n(D) Maximum charge on capacitor Co is 2.4 \u00d7 10^-12 coulomb", "answer": "", "page_number": 8, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 16, "question": "A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration a along a fixed inclined plane with angle \u03b8 = 45\u00b0. P1 and P2 are pressures at points 1 and 2, respectively, located at the base of the tube. Let \u03b2 = (P1 \u2212 P2)/(\u03c1gd), where \u03c1 is density of water, d is the inner diameter of the tube and g is the acceleration due to gravity. Which of the following statement(s) is(are) correct?", "response_choices": "A) \u03b2 = 0 when a = g/\u221a2, B) \u03b2 > 0 when a = g/\u221a2, C) \u03b2 = \u221a2-1/\u221a2 when a = g/2, D) \u03b2 = 1/\u221a2 when a = g/2", "answer": "", "page_number": 9, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 17, "question": "An \u03b1-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the \u03b1-particle and the sulfur ion move in circular orbits of radii r\u03b1 and rS, respectively. The ratio (rS/r\u03b1) is ___.", "response_choices": "", "answer": "", "page_number": 10, "image_available": "no", "question_subject": "physics"} | |
| {"id": 18, "question": "A thin rod of mass M and length a is free to rotate in horizontal plane about a fixed vertical axis passing through point O. A thin circular disc of mass M and of radius a/4 is pivoted on this rod with its center at a distance a/4 from the free end so that it can rotate freely about its vertical axis, as shown in the figure. Assume that both the rod and the disc have uniform density and they remain horizontal during the motion. An outside stationary observer finds the rod rotating with an angular velocity \u03a9 and the disc rotating about its vertical axis with angular velocity 4\u03a9. The total angular momentum of the system about the point O is (Ma^2\u03a9)/48 n. The value of n is ___.", "response_choices": "", "answer": "", "page_number": 10, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 19, "question": "A small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at 0 K. At time t = 0, the temperature of the object is 200 K. The temperature of the object becomes 100 K at t = t1 and 50 K at t = t2. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio (t2/t1) is ____.", "response_choices": "No response choices provided.", "answer": "____", "page_number": 11, "image_available": "no", "question_subject": "physics"} | |
| {"id": 3, "question": "For the given close packed structure of a salt made of cation X and anion Y shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction = packing efficiency/100)", "response_choices": "(A) 0.74, (B) 0.63, (C) 0.52, (D) 0.48", "answer": "C", "page_number": 13, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 4, "question": "The calculated spin only magnetic moments of [Cr(NH3)6]3+ and [CuF6]3- in BM, respectively, are (Atomic numbers of Cr and Cu are 24 and 29, respectively)", "response_choices": "(A) 3.87 and 2.84, (B) 4.90 and 1.73, (C) 3.87 and 1.73, (D) 4.90 and 2.84", "answer": "B", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 5, "question": "The value of x is ___.", "response_choices": "", "answer": "", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 6, "question": "The value of y is ___.", "response_choices": "", "answer": "", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 7, "question": "The value of standard enthalpy, \u0394H\u00b0 (in kJ mol\u207b\u00b9) for the given reaction is ___.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 8, "question": "The value of \u0394S\u00b0 (in J K\u207b\u00b9 mol\u207b\u00b9) for the given reaction, at 1000 K is ___.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 9, "question": "The boiling point of water in a 0.1 molal silver nitrate solution (solution A) is x \u00b0C. To this solution A, an equal volume of 0.1 molal aqueous barium chloride solution is added to make a new solution B. The difference in the boiling points of water in the two solutions A and B is y \u00d7 10\u207b\u00b2 \u00b0C.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 10, "question": "Follow up from Question 9, no additional details provided.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 9, "question": "The value of x is ___.", "response_choices": "", "answer": "", "page_number": 16, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 10, "question": "The value of |y| is ___.", "response_choices": "", "answer": "", "page_number": 16, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 11, "question": "The compound(s), which on reaction with HNO3 will give the product having degree of rotation, [\u03b1]D = \u221252.7\u00b0 is(are)", "response_choices": "(A), (B), (C), (D)", "answer": "(D)", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 12, "question": "The reaction of Q with PhSNa yields an organic compound (major product) that gives positive Carius test on treatment with Na2O2 followed by addition of BaCl2. The correct option(s) for Q is(are)", "response_choices": "(A), (B), (C), (D)", "answer": "(C)", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 13, "question": "The correct statement(s) related to colloids is(are)", "response_choices": "(A) The process of precipitating colloidal sol by an electrolyte is called peptization. (B) Colloidal solution freezes at higher temperature than the true solution at the same concentration. (C) Surfactants form micelle above critical micelle concentration (CMC). CMC depends on temperature. (D) Micelles are macromolecular colloids.", "answer": "", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 14, "question": "An ideal gas undergoes a reversible isothermal expansion from state I to state II followed by a reversible adiabatic expansion from state II to state III. The correct plot(s) representing the changes from state I to state III is(are)", "response_choices": "(A) (B) (C) (D)", "answer": "B", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 15, "question": "The correct statement(s) related to the metal extraction processes is(are)", "response_choices": "(A) A mixture of PbS and PbO undergoes self-reduction to produce Pb and SO2. (B) In the extraction process of copper from copper pyrites, silica is added to produce copper silicate. (C) Partial oxidation of sulphide ore of copper by roasting, followed by self-reduction produces blister copper. (D) In cyanide process, zinc powder is utilized to precipitate gold from Na[Au(CN)2].", "answer": "", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 16, "question": "A mixture of two salts is used to prepare a solution S, which gives the following results:", "response_choices": "(A) Pb(NO3)2 and Zn(NO3)2 (B) Pb(NO3)2 and Bi(NO3)3 (C) AgNO3 and Bi(NO3)3 (D) Pb(NO3)2 and Hg(NO3)2", "answer": "", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 17, "question": "The maximum number of possible isomers (including stereoisomers) which may be formed on mono-bromination of 1-methylcyclohex-1-ene using Br2 and UV light is ___.", "response_choices": "", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 18, "question": "In the reaction given below, the total number of atoms having sp2 hybridization in the major product P is ___.", "response_choices": "", "answer": "", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 19, "question": "The total number of possible isomers for [Pt(NH3)4Cl2]Br2 is ___.", "response_choices": "", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 1, "question": "Consider a triangle A whose two sides lie on the x-axis and the line x + y + 1 = 0. If the orthocenter of A is (1, 1), then the equation of the circle passing through the vertices of the triangle A is", "response_choices": "(A) x^2 + y^2 - 3x + y = 0, (B) x^2 + y^2 + x + 3y = 0, (C) x^2 + y^2 + 2y - 1 = 0, (D) x^2 + y^2 + x + y = 0", "answer": "D", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 2, "question": "The area of the region {(x, y) : 0 \u2264 x \u2264 9/4, 0 \u2264 y \u2264 1, x \u2265 3y, x + y \u2265 2} is", "response_choices": "(A) 11/32, (B) 35/96, (C) 37/96, (D) 13/32", "answer": "C", "page_number": 22, "image_available": "yes", "question_subject": "mathematics"} | |
| {"id": 3, "question": "Consider three sets E1 = {1, 2, 3}, F1 = {1, 3, 4} and G1 = {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E1, and let S1 denote the set of these chosen elements. Let E2 = E1 - S1 and F2 = F1 \u222a S1. Now two elements are chosen at random, without replacement, from the set F2 and let S2 denote the set of these chosen elements. Let G2 = G1 \u222a S2. Finally, two elements are chosen at random, without replacement, from the set G2 and let S3 denote the set of these chosen elements. Let E3 = E2 \u222a S3. Given that E1= E3, let p be the conditional probability of the event S1 = {1, 2}. Then the value of p is", "response_choices": "(A) 1/5, (B) 2/5, (C) 1/2, (D) 2/5", "answer": "B", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 5, "question": "The value of (625/4) * p1 is ___.", "response_choices": "No multiple choice options provided", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 6, "question": "The value of (125/4) * p2 is ___.", "response_choices": "No multiple choice options provided", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 7, "question": "The value of |M| is __ .", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 8, "question": "The value of D is __ .", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 9, "question": "The value of \u03bb2 is __ .", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 10, "question": "The value of D is __ .", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 11, "question": "For any 3 \u00d7 3 matrix M, let |M| denote the determinant of M. Let E = [1 2 3; 2 3 4; 8 13 18], P = [1 0 0; 0 0 1; 0 1 0] and F = [1 3 2; 8 18 13; 2 4 3]. If Q is a nonsingular matrix of order 3 \u00d7 3, then which of the following statements is (are) TRUE?", "response_choices": "Options A, B, C, D (not provided in the image)", "answer": "Not provided", "page_number": 26, "image_available": "yes", "question_subject": "mathematics"} | |
| {"id": 1, "question": "(A) F = PEP and P^2 = [1 0 0; 0 1 0; 0 0 1] (B) |EQ + PFQ^-1| = |EQ| + |PFQ^-1| (C) |(EF)^3| > |EF|^2 (D) Sum of the diagonal entries of P^-1FP + F is equal to the sum of diagonal entries of E + P^-1FP", "response_choices": "No options given", "answer": "No answer given", "page_number": 27, "image_available": "yes", "question_subject": "mathematics"} | |
| {"id": 2, "question": "Let f: R \u2192 R be defined by f(x) = (x^2 - 3x - 6) / (x^2 + 2x + 4). Then which of the following statements is (are) TRUE? (A) f is decreasing in the interval (-2, -1) (B) f is increasing in the interval (1, 2) (C) f is onto (D) Range of f is [-3/2, 2]", "response_choices": "(A), (B), (C), (D)", "answer": "No answer given", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 3, "question": "Let E, F and G be three events having probabilities P(E) = 1/8, P(F) = 1/6 and P(G) = 1/4, and let P(E \u2229 F \u2229 G) = 1/10. For any event H, if H^c denotes its complement, then which of the following statements is (are) TRUE? (A) P(E \u2229 F \u2229 G^c) \u2264 1/40 (B) P(E^c \u2229 F \u2229 G) \u2264 1/15 (C) P(E \u222a F \u222a G) \u2264 13/24 (D) P(E^c \u2229 F^c \u2229 G^c) \u2264 5/12", "response_choices": "(A), (B), (C), (D)", "answer": "No answer given", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 4, "question": "For any 3 \u00d7 3 matrix M, let |M| denote the determinant of M. Let I be the 3 \u00d7 3 identity matrix. Let E and F be two 3 \u00d7 3 matrices such that (I - EF) is invertible. If G = (I - EF)^-1, then which of the following statements is (are) TRUE? (A) |FE| = |I - FE||FGE| (B) (I - FE)(I + FGE) = I", "response_choices": "(A), (B)", "answer": "No answer given", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 15, "question": "For any positive integer n, let Sn: (0,\u221e) \u2192 \u211d be defined by Sn(x) = \u2211(n)(k=1) cot^(-1)((1 + k(k + 1)x^2)/x), where for any x \u2208 \u211d, cot^(-1)(x) \u2208 (0,\u03c0) and tan^(-1)(x) \u2208 (-\u03c0/2,\u03c0/2). Then which of the following statements is (are) TRUE?", "response_choices": "(A) S10(x) = \u03c0/2 = tan^(-1)((1+11x^2)/(10x)), for all x > 0\n(B) lim cot(Sn(x)) = x, for all x > 0\nn\u2192\u221e\n(C) The equation S3(x) = \u03c0/4 has a root in (0,\u221e)\n(D) tan(Sn(x)) \u2264 1/2, for all n \u2265 1 and x > 0", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 16, "question": "For any complex number w = c + id, let arg(w) \u2208 (-\u03c0,\u03c0], where i = \u221a(-1) . Let \u03b1 and \u03b2 be real numbers such that for all complex numbers z = x + iy satisfying arg((z+\u03b1)/(z+\u03b2)) = \u03c0/4, the ordered pair (x,y) lies on the circle x^2 + y^2 + 5x - 3y + 4 = 0. Then which of the following statements is (are) TRUE?", "response_choices": "(A) \u03b1 = -1\n(B) \u03b1\u03b2 = 4\n(C) \u03b1\u03b2 = -4\n(D) \u03b2 = 4", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 17, "question": "For x \u2208 \u211d, the number of real roots of the equation 3x^2 - 4|x^2 - 1| + x - 1 = 0 is ___.", "response_choices": "None provided", "answer": "Must enter an integer", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 18, "question": "In a triangle ABC, let AB = \u221a23, BC = 3 and CA = 4. Then the value of (cot A + cot C) / cot B is ___.", "response_choices": "None provided", "answer": "Must enter an integer", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 19, "question": "Let \u20d7u, \u20d7v and \u20d7w be vectors in three-dimensional space, where \u20d7u and \u20d7v are unit vectors which are not perpendicular to each other and \u20d7u \u00b7 \u20d7w = 1, \u20d7v \u00b7 \u20d7w = 1, \u20d7w \u00b7 \u20d7w = 4 If the volume of the parallelopiped, whose adjacent sides are represented by the vectors \u20d7u, \u20d7v and \u20d7w, is \u221a2 , then the value of |3 \u20d7u +5 \u20d7v | is ___.", "response_choices": "None provided", "answer": "Must enter an integer", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} | |